This project is designed to investigate the role that individual observations or cases play in controlling data analyses based on full rank linear models. Primary emphasis is on developing and comparing measures of influence for groups of cases and for combinations of parameters, such as predictions, developing measures of influence for secondary phases of the analyses, such as subset regression, and on defining a region of applicability for a fitted model. Comparison of results to those obtained using non-least squares methodology is also studied. These problems can be important in the analyses of data obtained from a wide variety of bio-medical applications, such as clinical trials.